First-principles calculations are used to explore the strong binding of lithium to boron- and carbon-doped BC2N monolayers (BC2NBC and BC2NCN, respectively) without the formation of lithium clusters. In comparison to BC2N and BC2NCB, lithium-decorated BC2NBC and BC2NCN systems possess stronger s-p and p-p hybridization and, hence, the binding energy is higher. Lithium becomes partially positively charged by donating electron density to the more electronegative atoms of the sheet. Attractive van der Waals interactions are responsible for binding hydrogen molecules around the lithium atoms. Each lithium atom can adsorb three hydrogen molecules on both sides of the sheet, with an average hydrogen binding energy of approximately 0.2 eV, which is in the range required for practical applications. The BC2NBC-Li and BC2NCN-Li complexes can serve as high-capacity hydrogen-storage media with gravimetric hydrogen capacities of 9.88 and 9.94 wt %, respectively.